Markov Potential Game Construction and Multi-Agent Reinforcement Learning with Applications to Autonomous Driving

Markov games (MGs) provide a mathematical foundation for multi-agent reinforcement learning (MARL), enabling self-interested agents to learn their optimal policies while interacting with others in a shared environment. However, due to the complexities of an MG problem, seeking (Markov perfect) Nash equilibrium (NE) is often very challenging for a general-sum MG. Markov potential games (MPGs), which are a special class of MGs, have appealing properties such as guaranteed existence of pure NEs and guaranteed convergence of gradient play algorithms, thereby leading to desirable properties for many MARL algorithms in their NE-seeking processes. However, the question of how to construct MPGs has remained open. This paper provides sufficient conditions on the reward design and on the Markov decision process (MDP), under which an MG is an MPG. Numerical results on autonomous driving applications are reported.